Chapter 2:
Soon after posting “Learning Is about Making Connections,” I sensed the power of posting a Big Idea, and felt the need to identify additional Big Ideas. However, I had not yet traveled enough of a reflective journey to sense what the next Big Idea might be. Even so, I felt the need for an example that I could quickly reference.
I needed something that could help to further ground the concept of connections.
I posted an idea that featured what I assumed to be a very simple connection.
“Girls and boys, we know that learning is about making connections. I’d like to give you an example. Addition and subtraction are connected.”
Then I proceeded to write a graphic on the board that has been used in many classrooms far and wide.
“We can see here how addition and subtraction are connected. This is an idea that you learned years ago, but our Big Idea is that learning is about making connections. Let’s find out more. Let’s make some connections.”
And with that, I launched into a series of questions.
Seeking more connections, we began exploring the relationships among all three numbers. I offered more questions to the students.
We also began exploring what may or may not be true.
“If we add one to every number in the triangle, will the relationships stand? Why or why not? What if we subtract one from every number in the triangle? Will those relationships be true? Why or why not?”
Learning is about making connections, so we dug even deeper. “What if we only change two numbers in the triangle? Are there any cases in which we can add one to two of the numbers in the triangle and maintain a valid relationship? Does this also work with subtraction? What does that tell us about how addition and subtraction are connected?”
Then I presented another question that earlier might have simply produced a number, but we were looking much deeper at this point.
The Big Idea, coupled with the graphics, helped us to see more clearly how learning is about making connections. Admittedly, the relationship between addition and subtraction was not a profound idea that was destined to deeply impact our classroom culture. Yet the context was extremely useful. The example helped us to understand that learning connections are abundant, available, and within reach. It also helped us to recognize the importance of looking a little deeper to find those connections.
Most importantly, our pursuit of connections changed the atmosphere in the classroom. Seeking unexpected connections was empowering and invigorating. We began to hunger for those connections.
Of the many, many lessons that my students continued to teach me, one very useful lesson was that there is great power in simply posting an image alongside a question. There is great value in allowing the opportunity which that question provides to remain available to students over the course of many days, weeks, or even months.
Instead of erasing images, I began sketching them on pieces of paper and posting them in places where students could think about them. I might post an image exactly like this, with a simple statement, such as, “I’m interested in how doubling and halving are related to this image.”
I learned that there is great power in letting opportunities linger.
Allowing opportunities to linger invites wonder and insight.
With images positioned where they could tantalize the students’ curiosity, we traveled through the day. Sometimes those images remained dormant for hours or days. At other times, they sprung to life as students responded to them.
When I look back on Big Idea 2, an idea which I nearly took off the wall later, I now understand that its greatest contribution to our classroom community was that it started the momentum that led to a journey. It became a paving stone, leading across a largely empty wall, and it pointed toward more empty spaces.
The first Big Idea was an extremely important experience.
The second Big Idea provided the momentum that carried the journey forward.